As a result of this, the simulation run time can be reduced significantly.
Consider the following weight function assuming Gaussian noise statistics:
(8.43)
(8.44)
Typical literature notations use the following, with :
(8.45)
Since we fix the IS parameter prior to simulating, the weight function is a simple equation (assuming
the Gaussian PDF).
s2
s2*
1 a
0 a 1
w(nk)
s*
s
# e[1s2/s2
*]n2
k /2s2
w(nk)
fN(nk)
f *
N (nk)
1
s12p
# en2
k/2s2
1
s*12p
# en2
k/2s2
*
s2*
s2
COMPUTER SIMULATION ESTIMATION TECHNIQUES 467
Noise
Filter Modulator
Delay
+ Filter Demodulator
Error
Counting
Memory Size of M Samples
Bits in Bits out
FIGURE 8.7 Modified digital communication simulation block diagram.
f *
N(n)
fN (n)
0
n
FIGURE 8.8 IS biasing.
In order to quantify the performance improvement, let??™s define the sample size reduction factor r as
(8.46)
Equivalently, it can be expressed using the noise PDF function, with .
(8.47)
This variance-scaling technique can be visualized as follows: You specify a certain SNR; let??™s say
SNR1 is the desired point of interest.
(8.48)
The simulation SNR is actually lower due to the increased noise variance
(8.49)
This can be better understood with the BER performance curve in Fig.
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